# Quickest Detection

### 1 Rationale

This is a comprehensive course on the topic of quickest detection that has

been oered at the Graduate Center since the Fall of 2008. It covers the fun-

damental theory of quickest detection, the algorithms associated with it and

the applications of quickest detection in a variety of elds, namely nance,

signal processing and 3D Computer Vision. The basic nancial notions of

asset pricing and risk are also discussed. There is a great commitment in

research and a huge commercial interest in all of the application areas on

this eld. A number of graduate students in the PhD program are currently

using such algorithms in their research.

### 2 Course Description

The problem of detecting abrupt changes in the statistical behavior of obser-

vation arises in a variety of elds including signal processing, computer vision

and nance. Using the mathematical methods of statistical sequential tech-

niques and stochastic optimization, this course describes the fundamentals

underpinning the eld providing the background necessary to design analyze

and understand quickest detection algorithms and stopping times. In this

course we will provide a unied treatment of several dierent approaches to

the quickest detection problem and draw examples from the eld of signal

processing, nance and computer vision. The course also covers models used

in nance and signal processing, brownian motion, Ito calculus, markov pro-

cesses and the fundamental theory of asset pricing. The notion of stopping

time and its association with detection algorithms is further examined. More-

over, connections between detection algorithms and drawdown measures are

drawn. The course nally examines the use of detection algorithms in on-

line trading and the detection and classication of objects in point clouds of

urban scenes.

### 3 Topic List

Topics may include but are not limited to:

• Statistical and sequential hypothesis testing
• The sequential probability ratio test and the cumulative sum algorithms as stopping times
• Applications to computer vision, algorithmic trading and signal processing
• Modeling in nance and signal processing, brownian motion
• Ito calculus, martingales, markov processes and the fundamental theory of asset pricing
• Drawdowns measures of risk and connections to detection

### 4 Learning Goals

• A general understanding of the importance of quickest detection in various fields.
• Understanding of the notion of stopping time and online detection
• Ability to formulate research questions and to write research reports
• Ability to present technical talks
• Understanding of selected detection algorithms and how they can be applied in various elds
• Knowledge of basic models and stochastic processes used in signal processing and finance
• Knowledge of the fundamental theory of asset pricing, the notion of risk and how it relates to drawdowns and detection

### 5 Assessment

The course requires a midterm exam, a project and a nal. Each student will

prepare a research report either related to the theoretical study of detection

algorithms or to adjusting and applying detection algorithms in a topic of

their choice. The report will also be supported by a student presentation

in class. Grading will be based on the attendance, student presentation,

midterm, nal and the nal research report and project. Students can work

in groups if they desire so for the nal project, upon the consent of the

instructor. I will provide a list of possible topics that would be appropriate

for the nal project and report. Student can pick a topic from this list or

can also work on any other related topic of their choice subject to instructor

approval.